A smooth sphere B of mass $3$ kg strikes a fixed vertical wall at right angles, moving at $2\,\mathrm{ms^{-1}}$ . The coefficient of restitution is $\dfrac14$ . Find the speed at which B rebounds, in $\mathrm{ms^{-1}}$ .

Model answer

0.5

Also accepted: 0.5 m/s, 0.50, 1/2

Explanation

The wall is fixed, so its speed is zero before and after. The law of restitution then gives the rebound speed as

e

times the approach speed:

\dfrac14 \times 2 = 0.5\,\mathrm{ms^{-1}}

, directed away from the wall.

Derived from ZIMSEC Additional Mathematics Paper 2, Specimen Paper, Q5

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